Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 16 Dec 2007 04:49:08 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/16/t1197804839gmder80i2p4bsyq.htm/, Retrieved Sat, 07 Feb 2026 03:14:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4141, Retrieved Sat, 07 Feb 2026 03:14:19 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

433

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [graan] [2007-12-16 11:49:08] [a98121933c09d0d44a9f89053acd1df1] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4141&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4141&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4141&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	9.5917	0
1	0.254006	2.4363	0.008381
2	-0.020662	-0.1982	0.578329
3	0.12328	1.1825	0.120035
4	-0.086352	-0.8283	0.795166
5	-0.20796	-1.9947	0.975481
6	-0.133369	-1.2792	0.897983
7	0.070954	0.6806	0.248928
8	0.038073	0.3652	0.357905
9	0.004042	0.0388	0.48458
10	0.088745	0.8512	0.198431
11	0.097191	0.9322	0.176831
12	-0.012132	-0.1164	0.546192
13	-0.043515	-0.4174	0.661313
14	0.011179	0.1072	0.457423
15	-0.010035	-0.0963	0.538235
16	0.170724	1.6375	0.052468
17	0.017497	0.1678	0.433546
18	0.062682	0.6012	0.274584

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.5917 & 0 \tabularnewline
1 & 0.254006 & 2.4363 & 0.008381 \tabularnewline
2 & -0.020662 & -0.1982 & 0.578329 \tabularnewline
3 & 0.12328 & 1.1825 & 0.120035 \tabularnewline
4 & -0.086352 & -0.8283 & 0.795166 \tabularnewline
5 & -0.20796 & -1.9947 & 0.975481 \tabularnewline
6 & -0.133369 & -1.2792 & 0.897983 \tabularnewline
7 & 0.070954 & 0.6806 & 0.248928 \tabularnewline
8 & 0.038073 & 0.3652 & 0.357905 \tabularnewline
9 & 0.004042 & 0.0388 & 0.48458 \tabularnewline
10 & 0.088745 & 0.8512 & 0.198431 \tabularnewline
11 & 0.097191 & 0.9322 & 0.176831 \tabularnewline
12 & -0.012132 & -0.1164 & 0.546192 \tabularnewline
13 & -0.043515 & -0.4174 & 0.661313 \tabularnewline
14 & 0.011179 & 0.1072 & 0.457423 \tabularnewline
15 & -0.010035 & -0.0963 & 0.538235 \tabularnewline
16 & 0.170724 & 1.6375 & 0.052468 \tabularnewline
17 & 0.017497 & 0.1678 & 0.433546 \tabularnewline
18 & 0.062682 & 0.6012 & 0.274584 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4141&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]0[/C][C]1[/C][C]9.5917[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.254006[/C][C]2.4363[/C][C]0.008381[/C][/ROW]
[ROW][C]2[/C][C]-0.020662[/C][C]-0.1982[/C][C]0.578329[/C][/ROW]
[ROW][C]3[/C][C]0.12328[/C][C]1.1825[/C][C]0.120035[/C][/ROW]
[ROW][C]4[/C][C]-0.086352[/C][C]-0.8283[/C][C]0.795166[/C][/ROW]
[ROW][C]5[/C][C]-0.20796[/C][C]-1.9947[/C][C]0.975481[/C][/ROW]
[ROW][C]6[/C][C]-0.133369[/C][C]-1.2792[/C][C]0.897983[/C][/ROW]
[ROW][C]7[/C][C]0.070954[/C][C]0.6806[/C][C]0.248928[/C][/ROW]
[ROW][C]8[/C][C]0.038073[/C][C]0.3652[/C][C]0.357905[/C][/ROW]
[ROW][C]9[/C][C]0.004042[/C][C]0.0388[/C][C]0.48458[/C][/ROW]
[ROW][C]10[/C][C]0.088745[/C][C]0.8512[/C][C]0.198431[/C][/ROW]
[ROW][C]11[/C][C]0.097191[/C][C]0.9322[/C][C]0.176831[/C][/ROW]
[ROW][C]12[/C][C]-0.012132[/C][C]-0.1164[/C][C]0.546192[/C][/ROW]
[ROW][C]13[/C][C]-0.043515[/C][C]-0.4174[/C][C]0.661313[/C][/ROW]
[ROW][C]14[/C][C]0.011179[/C][C]0.1072[/C][C]0.457423[/C][/ROW]
[ROW][C]15[/C][C]-0.010035[/C][C]-0.0963[/C][C]0.538235[/C][/ROW]
[ROW][C]16[/C][C]0.170724[/C][C]1.6375[/C][C]0.052468[/C][/ROW]
[ROW][C]17[/C][C]0.017497[/C][C]0.1678[/C][C]0.433546[/C][/ROW]
[ROW][C]18[/C][C]0.062682[/C][C]0.6012[/C][C]0.274584[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4141&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4141&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	9.5917	0
1	0.254006	2.4363	0.008381
2	-0.020662	-0.1982	0.578329
3	0.12328	1.1825	0.120035
4	-0.086352	-0.8283	0.795166
5	-0.20796	-1.9947	0.975481
6	-0.133369	-1.2792	0.897983
7	0.070954	0.6806	0.248928
8	0.038073	0.3652	0.357905
9	0.004042	0.0388	0.48458
10	0.088745	0.8512	0.198431
11	0.097191	0.9322	0.176831
12	-0.012132	-0.1164	0.546192
13	-0.043515	-0.4174	0.661313
14	0.011179	0.1072	0.457423
15	-0.010035	-0.0963	0.538235
16	0.170724	1.6375	0.052468
17	0.017497	0.1678	0.433546
18	0.062682	0.6012	0.274584

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.254006	2.4363	0.008381
1	-0.091056	-0.8734	0.807634
2	0.163987	1.5729	0.059587
3	-0.184799	-1.7725	0.960191
4	-0.124711	-1.1962	0.882651
5	-0.091373	-0.8764	0.808458
6	0.161893	1.5528	0.061949
7	-0.002801	-0.0269	0.510688
8	0.010716	0.1028	0.459178
9	-0.000113	-0.0011	0.500432
10	0.062278	0.5974	0.27587
11	-0.024859	-0.2384	0.593965
12	-0.005833	-0.0559	0.522247
13	0.002941	0.0282	0.48878
14	0.013375	0.1283	0.449099
15	0.250937	2.4069	0.009043
16	-0.13942	-1.3373	0.907784
17	0.133	1.2757	0.102638
18	-0.024525	-0.2352	0.592725

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.254006 & 2.4363 & 0.008381 \tabularnewline
1 & -0.091056 & -0.8734 & 0.807634 \tabularnewline
2 & 0.163987 & 1.5729 & 0.059587 \tabularnewline
3 & -0.184799 & -1.7725 & 0.960191 \tabularnewline
4 & -0.124711 & -1.1962 & 0.882651 \tabularnewline
5 & -0.091373 & -0.8764 & 0.808458 \tabularnewline
6 & 0.161893 & 1.5528 & 0.061949 \tabularnewline
7 & -0.002801 & -0.0269 & 0.510688 \tabularnewline
8 & 0.010716 & 0.1028 & 0.459178 \tabularnewline
9 & -0.000113 & -0.0011 & 0.500432 \tabularnewline
10 & 0.062278 & 0.5974 & 0.27587 \tabularnewline
11 & -0.024859 & -0.2384 & 0.593965 \tabularnewline
12 & -0.005833 & -0.0559 & 0.522247 \tabularnewline
13 & 0.002941 & 0.0282 & 0.48878 \tabularnewline
14 & 0.013375 & 0.1283 & 0.449099 \tabularnewline
15 & 0.250937 & 2.4069 & 0.009043 \tabularnewline
16 & -0.13942 & -1.3373 & 0.907784 \tabularnewline
17 & 0.133 & 1.2757 & 0.102638 \tabularnewline
18 & -0.024525 & -0.2352 & 0.592725 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4141&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]0[/C][C]0.254006[/C][C]2.4363[/C][C]0.008381[/C][/ROW]
[ROW][C]1[/C][C]-0.091056[/C][C]-0.8734[/C][C]0.807634[/C][/ROW]
[ROW][C]2[/C][C]0.163987[/C][C]1.5729[/C][C]0.059587[/C][/ROW]
[ROW][C]3[/C][C]-0.184799[/C][C]-1.7725[/C][C]0.960191[/C][/ROW]
[ROW][C]4[/C][C]-0.124711[/C][C]-1.1962[/C][C]0.882651[/C][/ROW]
[ROW][C]5[/C][C]-0.091373[/C][C]-0.8764[/C][C]0.808458[/C][/ROW]
[ROW][C]6[/C][C]0.161893[/C][C]1.5528[/C][C]0.061949[/C][/ROW]
[ROW][C]7[/C][C]-0.002801[/C][C]-0.0269[/C][C]0.510688[/C][/ROW]
[ROW][C]8[/C][C]0.010716[/C][C]0.1028[/C][C]0.459178[/C][/ROW]
[ROW][C]9[/C][C]-0.000113[/C][C]-0.0011[/C][C]0.500432[/C][/ROW]
[ROW][C]10[/C][C]0.062278[/C][C]0.5974[/C][C]0.27587[/C][/ROW]
[ROW][C]11[/C][C]-0.024859[/C][C]-0.2384[/C][C]0.593965[/C][/ROW]
[ROW][C]12[/C][C]-0.005833[/C][C]-0.0559[/C][C]0.522247[/C][/ROW]
[ROW][C]13[/C][C]0.002941[/C][C]0.0282[/C][C]0.48878[/C][/ROW]
[ROW][C]14[/C][C]0.013375[/C][C]0.1283[/C][C]0.449099[/C][/ROW]
[ROW][C]15[/C][C]0.250937[/C][C]2.4069[/C][C]0.009043[/C][/ROW]
[ROW][C]16[/C][C]-0.13942[/C][C]-1.3373[/C][C]0.907784[/C][/ROW]
[ROW][C]17[/C][C]0.133[/C][C]1.2757[/C][C]0.102638[/C][/ROW]
[ROW][C]18[/C][C]-0.024525[/C][C]-0.2352[/C][C]0.592725[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4141&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4141&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.254006	2.4363	0.008381
1	-0.091056	-0.8734	0.807634
2	0.163987	1.5729	0.059587
3	-0.184799	-1.7725	0.960191
4	-0.124711	-1.1962	0.882651
5	-0.091373	-0.8764	0.808458
6	0.161893	1.5528	0.061949
7	-0.002801	-0.0269	0.510688
8	0.010716	0.1028	0.459178
9	-0.000113	-0.0011	0.500432
10	0.062278	0.5974	0.27587
11	-0.024859	-0.2384	0.593965
12	-0.005833	-0.0559	0.522247
13	0.002941	0.0282	0.48878
14	0.013375	0.1283	0.449099
15	0.250937	2.4069	0.009043
16	-0.13942	-1.3373	0.907784
17	0.133	1.2757	0.102638
18	-0.024525	-0.2352	0.592725

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

R code (references can be found in the software module):

if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code